Cumulative relative frequency is found by sequentially adding the relative frequencies of each class or category. The relative frequency of a category is the proportion of times it occurs in a data set. You calculate it by dividing the frequency of that category by the total number of observations. The cumulative relative frequency for a given category is then the sum of its relative frequency and the relative frequencies of all categories before it.
Here's a step-by-step breakdown of how to calculate it, based on the reference:
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Calculate the Relative Frequency: For each category, divide the frequency (count) of the category by the total number of observations in your dataset.
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Calculate the First Cumulative Relative Frequency: The cumulative relative frequency of the first category is the same as its relative frequency since there are no prior values to add.
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Calculate Subsequent Cumulative Relative Frequencies:
- Take the cumulative relative frequency of the previous category.
- Add the relative frequency of the current category to that number.
- The result is the cumulative relative frequency of the current category.
- Repeat this process for all categories, adding each successive relative frequency to the prior cumulative value.
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The last Cumulative Relative Frequency: The final cumulative relative frequency will equal 1, or 100%, if all values are included.
Example
Let's consider an example where the relative frequencies have already been computed:
| Category | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|
| A | 0.52 | 0.52 |
| B | 0.16 | 0.52 + 0.16 = 0.68 |
| C | 0.12 | 0.68 + 0.12 = 0.80 |
| D | 0.20 | 0.80 + 0.20 = 1.00 |
As the reference indicates, the cumulative relative frequency for category B is calculated by adding its relative frequency (0.16) to the cumulative relative frequency of the preceding category A (0.52), giving 0.68. This is the same for each of the other categories, where the new relative frequency is added to the previous cumulative value.
Key points
- Cumulative relative frequency can be presented in a table or graph.
- The values will always increase from 0 to 1 (or from 0% to 100%).
- It provides valuable insights into the distribution of data and where most of the data falls.
